Question

A couple deposits $20,000 into an account earning 7% annual interest for 20 years. Calculate thefuture value of the investment if the interest is compounded semiannually. Round your answer to thenearest cent.

Answer 1

Given

`\begin{gathered} Principal(P)=20,000 \\ r=7\%=(7)/(100)=0.07 \\ t=20 \end{gathered}`

To Determine: The future value of the investment

Solution

It can be observed that the deposit is compouned semi-annually

Step 1: Write out the formula

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=future\text{ value} \\ n=2(i.e.\text{ semi-annually means twice a year\rparen} \end{gathered}`

Step 2: SUbstitute the given into the formula

`\begin{gathered} A=20000(1+(0.07)/(2))^(2*20) \\ A=20000(1+0.035)^(40) \end{gathered}`
`\begin{gathered} A=20000(1.035)^(40) \\ A=20000(3.95925972117) \\ A=79185.19444 \\ A\approx79,185.19(nearest\text{ cent\rparen} \end{gathered}`

Hence, the future value of the investment is $79,185.19